In order to control the trajectory of the incoming particles and guide them towards the desired trap unit, a deviation system using six pairs of liquid electrodes similar to the one presented by Demierre et al. (2007) was placed upstream of the trapping chamber. Only two pairs of liquid electrodes are represented on the left of Figure 2A. Liquid electrodes are coplanar electrodes placed in a lateral recess from the main channel: this configuration guides the electric field and generate a vertical equipotential surface at the entrance of the main channel, hence the name “liquid electrodes”. Two sets of liquid electrodes combs are placed laterally on each side of the main channel and a voltage is applied to each set, with a phase shift of 180° to neighbouring electrodes. Each set of liquid electrodes generate a lateral DEP force uniform along the height of the channel pushing the particles away from them. The ratio of voltage applied to each side V ₁/V ₂ determines the equilibrium position along the y axis in the main channel, focusing the randomly distributed incoming particles towards a defined lateral position and deviating them towards the trap units, or to the bypass. As described by Demierre et al. (2007), the total force exerted on the particles is the sum of the forces exerted by each comb of electrodes and the particles are focused where these forces cancel each other: it is thus non dependent on the particle or cell size nor position before entering the deviation zone. At low fluid velocity, the limit in the focusing is due to particles collision and diffusion, which is compensated by the slanted part of the traps placed downstream, collecting particle streams covering 60 μm in width. The focusing nevertheless has a size dependent limit on the channel sides: the particle’s center cannot be focused closer to the wall than the particle’s radius due to straightforward reasons.

Two easy to fabricate configurations of counter electrodes were implemented and studied: a coplanar counter electrode which consists in a straight line electrode placed downstream of the trapping electrode as shown in Figure 2B, whereas for the facing counter-electrode, a conductive and transparent ITO layer is provided on the glass plate used to close the channels on their upper part as illustrated in Figure 2C. Both configurations are popular and extensively used to manipulate cells using DEP in microfluidic chips (Ho et al. (2013); Li and Bashir (2002); Morgan et al. (1999); Takahashi and Miyata (2020)). Other electrodes configurations that are known to create single cell traps comprise 3D electrodes (Keim et al., 2019) and strip electrodes (Seger et al., 2004), but such configurations are less accessible in terms of fabrication. In order to assess the three dimensional behaviour of the traps, both designs were simulated using COMSOL ⁽™⁾. Figure 3 illustrates the results of the simulation along the focus line indicated in Figure 2A: the colour indicates the magnitude of ∂ E 2 ∂ x , which is the electric field dependent factor that modulates the DEP force while the arrows of normalized size indicate the direction of the nDEP force along the x and z axis. Electrode locations are indicated on the results of simulations by black rectangles. Simulations indicate that both configurations can be used for the trapping of particles in three dimensions: the y component of the force directs the particles toward a single xz plane of equilibrium in the middle of each trapping unit (Supplementary Figure S1) while the z component pushes the particles towards the bottom of the channel. The x component of the DEP force counteracts the drag force. Its value, controlled by the applied voltage, determines the equilibrium position of the particles along the x direction. For the same voltage applied, the facing electrodes configuration generates a larger DEP force in the x direction compared to the coplanar configuration.

To test these two designs, chips with electrodes placed in both configurations and aligned to microfluidic channels with μm precision can be manufactured using standard cleanroom equipment with a few steps only. The fabrication process for both designs is detailed in the Materials and Methods section and illustrated in Figures 1A,B. Experiments are presented in the next section.

DEP can damage cells as it can induce a local rise in temperature. Indeed the presence of an electric field in a conductive media induces Joule heating. This effect can be mitigated by reducing the conductivity of the medium and correcting for osmolarity with the addition of dextrose or sucrose, but prolonged exposition of cells to such diluted media can alter their function and health (Hyler et al. (2021)). As both electrodes configurations presented here create a three dimensional DEP trap against the flow, we selected the most efficient configuration by measuring the magnitude of the DEP force against the flow for both configurations and evaluated in both cases the induced temperature rise. The expression of the time averaged DEP force exerted on a spherical particle in a non uniform electric field is given as follows: F DEP = 2 π ϵ m R 3 R e K ω ∇ E rms 2 (1) Where R is the radius of the particle, ϵ _m is the fluid permittivity, Re [K(ω)] is the real part of the Clausius-Mossotti factor and E _rms is the root mean square (rms) of the electric field. For a homogeneous spherical particle, the Clausius-Mossotti factor is given by the following formula: K ω = ϵ p ∗ − ϵ m ∗ ϵ p ∗ + 2 ϵ m ∗ (2) With ϵ p ∗ the complex permittivity of the particle and ϵ m ∗ the complex permittivity of the medium, which are both frequency dependent. The sign of the Clausius-Mossotti defines the regime of the DEP force, negative or positive, resulting in particles being respectively repulsed from or attracted to the high electric field regions. In this work, we operate at 100 kHz in the negative DEP regime and the real part of the Clausius-Mossotti factor has a value of −0.5 for all medium and particle or cell conditions.In order for a particle to be trapped, the projection of the DEP force on the axis of the flow direction (x in the present case) has to balance the viscous drag force exerted by the flow (Voldman et al. (2001); Rosenthal and Voldman (2005)): 6 π η R 6 v mean F ∗ z p h = 2 π ϵ m R 3 R e K ω ∂ E rms 2 ∂ x (3) Where η is the fluid viscosity, v _mean is the mean fluid velocity, h is the height of the channel, F* is a factor accounting for the wall effect, z _p is the height of the particle.

The heat flow generated by electrodes matches the electrical power input in the system and the average temperature around the DEP electrodes was shown to depend on the real part of the electrical power (Ramos et al., 1998; Seger-Sauli et al., 2005) which is defined as: P = V rms I rms ⁡ cos θ = V rms 2 Z cos θ (4) With V _rms the rms voltage applied to the electrodes, I _rms the rms electrical current, θ the phase shift between the current and voltage and Z the norm of the electrical impedance.

Since the temperature is directly proportional to the electrical power, this latter can be used as an indicator of electrodes trapping efficiency when comparing designs of similar size. Following Equation (3), the DEP force developed by a trap at steady state and at a defined position is directly proportional to the velocity of the fluid flow dragging the particle. We thus measured the maximum DEP force developed by each configuration by immobilizing a polystyrene particle in a trap at low fluid flow and increasing the flow until the bead is released. We measured the particle velocity at release, which is directly proportional to the maximum DEP force the trap can develop in the x direction at the edge of the electrode as a function of applied voltage and developed power. This latter is obtained by multiplying the applied voltage by the measured current at each condition following Eq. 4.

From Eq. 3, the mean velocity of the fluid can be expressed as: v mean = h 18 η F ∗ z p ϵ m R 2 R e K ω ∂ E rms 2 ∂ x (5)

Since the potential distribution in space is a direct function of the voltage V applied to the electrodes, we can derive that (see Supplementary Information) ∇ E rms 2 = α ( x , y , z ) V 2 , where α is a function of space. Eq. 5 can thus be re-written as: v mean = h 18 η F ∗ z p ϵ m R 2 R e K ω α x V 2 (6)

Introducing the electrical power into this equation from Eq. 4 we obtain: v mean = h 9 η F ∗ z p ⁡ cos θ ϵ m R 2 R e K ω α x Z P (7) With α _x the x component of α (x, y, z) described above and taken at the edge of the electrode, this equation indicates that the efficiency of trapping of a given design and configuration of electrodes depends on the multiplication of α _x and Z.

The current and phase were measured for both configurations and for voltage amplitudes between 1 and 10 V. The real part of the electrical power, responsible for Joule heating, was calculated as of Eq. 4. The mean and standard deviation phase was measured to be 11.2° and 1.4° respectively for the coplanar configuration and 8.9° and 1.5° respectively for the facing configuration, the real part of the power accounted for more than 97% of the apparent power thus indicating a mainly resistive load. Figure 4A is a plot of the measured speed at release for 5 μm in diameter polystyrene particles as a function of applied voltage amplitude for both facing and coplanar configurations. The dependency of the velocity at release is quadratic on the voltage in accordance with Eq. 6. As predicted by the simulations and Figure 3, the facing configuration generates a larger ∂ E rms 2 ∂ x for a given voltage and the velocity of the particle at release is larger in this configuration. Figure 4B shows the velocity at release as a function of electric active power. It results that the velocity at release depends linearly on the power as predicted from Eq. 7. It appears that the larger gradient factor α _x of the facing design does not compensate the smaller impedance of this design, resulting in more heat dissipated for a given DEP force than the coplanar design and thus a larger increase in temperature. The coplanar design was thus selected for the following study of cell trapping. However, the facing electrode configuration is suggested for applications where flow speed is the main criteria and heat generation is not a limitation since it generates a larger DEP force for a given voltage.

Electroporation can damage the cells when trapped using DEP. Electroporation takes place when the potential difference accross the cell membrane exceeds a threshold value, inducing pores in the membrane. This phenomenon is not necessarily lethal for the cells and is widely exploited to introduce genetic material inside the cells. However electroporation is not desired in manipulation applications and to avoid any damage to the cells we experimentally determined the applied voltage limit to avoid electroporation conditions. Jurkat cells were loaded with Calcein AM to visualize pore formation: as calcein is a volatile fluorescent molecule, it quickly diffuses out of the cell in case of pore formation in the membrane. The maximum velocity for trapping without electroporation as a function of voltage amplitude is measured and reported in Figure 5A. In case of fluorescence loss, the voltage was immediately turned off to release the cell and measure its speed. Events where a leak of calcein was observed are indicated by an orange circle, whereas events without fluorescence loss are indicated by a blue cross. A clear threshold under which no fluorescence loss is observed is found for a voltage of 5 V amplitude and determines the voltage operation limits to avoid cell damage. The large variation in speed at release can be explained by variations in cell size. Figure 5B is a picture of a cell arriving in the trap and Figure 5C shows the cell after fluorescence loss.

Typical transmembrane potential threshold above which pores appear have been reported between 0.25 and 1 V (Escoffre et al. (2011)). Schwan equation relates the transmembrane potential ΔΦ _m to the external alternating electric field E with angular frequency ω: Δ Φ m = 1.5 R E ⁡ cos φ 1 + ω τ 2 1 / 2 (8) Given τ = RC _mem (ρ _int + ρ _ext /2) with C _mem the membrane capacitance, ρ _int and ρ _ext the resistivity of respectively the internal and external fluid and φ the angle between the electric field lines and a line drawn from the center of the cell to the considered point of interest on the cell membrane. The critical value for transmembrane potential corresponds to a range of electric field between 2.8⋅10⁴ and 11.2⋅10⁴ V/m using membrane properties values from Reichle et al. (2000). Such values of electric field are found at the edge of the electrode and for a height of 5 μm in simulations for applied voltage amplitude ranging between 2.3 and 9.3 V and comprising the experimentally found threshold, consolidating the hypothesis of fluorescence leakage due to electroporation. The maximum voltage for cells manipulation without electroporation was thus set to 4 V amplitude. Larger voltages may be used without electroporating the cells as long as the flow drag force is limited and does not bring the cell in the critical electric field close to the electrode edge.

Different parameters were studied to understand their impact on the three-dimensional trapping property for an increased channel height. We defined the following parameters: d is the distance between the electrodes, l is the depth of the electrodes, h is the height of the channel and e is the width of the parallel part of the main electrode as illustrated on the inset of Figure 6. The angle of the slanted part was kept constant as well as the trap depth. Figure 6 is the result of COMSOL ™ simulations with the color indicating l o g 10 ( ∂ E 2 ∂ x ) , the black streamlines indicate the direction of the DEP vectors for different geometries. The magenta line indicates the contour of a null z component of the DEP force and thus separates the regions with upwards and downwards DEP force. A vertical contour defines a stable trap for a wide range of sizes and positions in the channel (Rosenthal and Voldman (2005)). Indeed, particles with a center of mass in the region with upward DEP force will be pushed upwards where the DEP force counteracting the flow is weaker, and therefore leave the trap. It is especially a problem when trapping multiple objects where the chance of finding an object higher in the channel is larger. As shown in the previous discussion, the standard design has a vertical contour and all particles coming in the traps will be pushed down to the floor. However, Figure 6B shows that this property is lost when keeping the same electrode geometry and increasing the channels height h. The scaling of the electrodes depth l and distance between them d is not enough to recover the vertical contour as seen on Figure 6C. A homothetic scaling is necessary to obtain the property of DEP force pushing down to a single equilibrium position along the whole trap height and to create a compact aggregate, as shown in Figure 6D.

We demonstrate here the ability of the presented system to create cell aggregates of controlled size and composition. The single cell design was scaled up as in Figure 6D to accommodate more cells in a channel height of 40 μm. Four parallel trapping units were placed next to each other and a bypass with no electrode was left next to the trapping units in order to discard unwanted cells. Two inlets were used sequentially to perfuse solutions with respectively Colo205 cells stained with blue calcein AM, and Jurkat cells stained with green calcein AM. The upstream deviation system was used to direct the incoming cells toward the desired trapping unit to create aggregates of 4 cells composed of three Colo205 and one Jurkat (Figures 7A–C) as well as two Colo205 and two Jurkat (Figures 7D–F). The calcein staining was used to both identify the cell type as well as to ensure cell viability. The aggregates could be held inside the traps up to 5 minutes without witnessing any leakage of the dye indicating membrane poration.